Pre Public Examination

GCSE Mathematics (Edexcel style) June 2017 Higher Tier Paper 3H

Worked Solutions

Name ……………………………………………………………… Class ………………………………………………………………

TIME ALLOWED 1 hour 30 minutes INSTRUCTIONS TO CANDIDATES

Answer all the questions.

Read each question carefully. Make sure you know what you have to

do before starting your answer.

You are permitted to use a calculator in this paper.

Do all rough work in this book.

INFORMATION FOR CANDIDATES

The number of marks is given in brackets [ ] at the end of each

question or part question on the Question Paper.

You are reminded of the need for clear presentation in your answers.

The total number of marks for this paper is 80. © The PiXL Club Limited 2017 This resource is strictly for the use of member schools for as long as they remain members of The

PiXL Club. It may not be copied, sold nor transferred to a third party or used by the school after

membership ceases. Until such time it may be freely used within the member school. All opinions

and contributions are those of the authors. The contents of this resource are not connected with nor

endorsed by any other company, organisation or institution.

Question

Mark

Out

of

1 2

2 3

3 4

4 6

5 4

6 3

7 6

8 3

9 5

10 4

11 4

12 7

13 3

14 4

15 3

16 5

17 4

18 5

19 5

Total 80

2

Answer ALL questions.

Write your answers in the spaces provided.

You must write down all the stages in your working.

Question 1.

A is the point with coordinates (7, 12)

B is the point with coordinates (-5, d)

The midpoint of the line is (1, 7.5)

Work out the value of d.

d = ................................

(Total 2 marks

Question 2.

Niel, Dan and Adam are friends.

Their ages are in the ratio 9 : 3 : 8

Niel is 6 years older than Adam.

What are their ages?

Niel……………………………...........

Dan…………………………………...

Adam…………………………………

(Total 3 marks)

3

Question 3.

(a) On the grid above, draw the line x = 2

(1)

(b) On the grid above, draw the line y = - x

(1)

x = 2

B1

y = -x

B1

4

(c) Find the gradient of the straight line drawn on this grid.

..........................................

(2)

(Total 4 marks)

1.5

1 M1

5

Question 4.

Fred has a recipe for 30 biscuits.

Here is a list of ingredients for 30 biscuits.

Fred wants to make 45 biscuits.

(a) Complete his new list of ingredients for 45 biscuits.

Self-raising flour…………………

Butter…………..…………………

Caster sugar………………………

Eggs………………………………

(3)

Gill has only 1 kilogram of self-raising flour.

She has plenty of the other ingredients.

(b) Work out the maximum number of biscuits that Gill could bake.

………………………………

(3)

(Total 6 marks)

Ingredients for 30 biscuits

Self-raising flour 230g

Butter 150g

Caster sugar 100g

Eggs 2

6

Question 5.

The diagram shows a circle with centre O and radius 2.5 cm.

TA is a tangent to the circle, of length 6 cm.

The line from A to the centre O of the circle cuts the circumference at B.

Calculate the length of AB.

………………………………

(Total 4 marks)

Diagram NOT

accurately drawn

7

Question 6.

Solve the simultaneous equations

5x + 2y = 22

10x + 9y = 59

(Total 3 marks)

8

Question 7.

A skip is in the shape of a prism with cross section ABCD.

AD = 2.3m, CD = 1.3m and BC = 1.7m.

The width of the skip is 1.5m.

(a) Calculate the volume of the skip.

………………………………

(3)

(b) Mr Brown has hired the skip to get rid of some rubbish from his garden.

The rubbish has a volume of 420cm3.

Will it all fit into the skip?

You must explain your answer.

………………………………………………………………………………..………………………………

………………………………………………………………………………..………………………………

………………………………………………………………………………..………………………………

………………………………………………………………………………..………………………………

(3)

(Total 6 marks)

Diagram NOT

accurately drawn

9

Question 8.

Dave and Anne each have an expression.

Show clearly that Dave’s expression is equivalent to Anne’s expression.

(Total 3 marks)

Dave

(x + 3)2 – 1

Anne

(x + 4) (x + 2)

10

Question 9.

The function f(x) and g(x) are shown below.

f(x) = 2x – 15 g(x) = x2 + c, where c is a constant.

(a) Find f(-6)

…………………………………………….

(1)

(b) Solve f(a) = 5

…………………………………………….

(2)

fg(4) = 25

(c) Use this to find the value of c.

…………………………………………….

(2)

(Total 5 marks)

11

Question 10.

E, F and G are points on the circumference of a circle with centre O.

FG = 13.3cm and angle EGF = 58°.

Calculate the circumference of the circle.

Give your answer to 3 significant figures.

(Total 4 marks)

58°

13.3cm

E

F G

Diagram NOT

accurately drawn

12

Question 11.

Aiysha has two bottles that are mathematically similar.

Aiysha says the big bottle will hold twice as much as the smaller bottle.

Is Aiysha right?

You must explain your answer.

(Total 4 marks)

Height = 15cm Height = 30cm

Capacity = 150ml

Diagram NOT

accurately drawn

13

Question 12.

Round a bend on a railway track the height difference (h mm) between the outer and inner rails must vary in

direct proportion to the square of the maximum permitted speed (S km/h).

(a) When S = 60, h = 45. Calculate h when S = 80.

h = …………………………………………….

(3)

(b) The maximum speed on a bend is to be increased by 30%. What will be the percentage increase in the

height difference between the outer and inner rails?

…………………………………………….

(4)

(Total 7 marks)

14

Question 13.

Given that x = 2.4 correct to 1 decimal place, find the interval that contains the value of 5x + 7.

Give your answer as an inequality.

…………………………………………….

(Total 3 marks)

Question 14.

A ruined tower is fenced off for safety reasons.

To find the height of the tower Ibrahim stands at a point A and measures the angle of elevation as 18°.

He then walks 20 metres directly towards the base of the tower to point B where the angle of elevation is

31°.

Calculate the height, h, of the tower to 2 decimal places.

(Total 4 marks)

Diagram NOT

accurately drawn

15

Question 15.

Use the iteration machine below with a starting value of x0 = 1 to find an approximation to the solution of

5x3 + 3x – 6 = 0 to 5 decimal places.

(Total 3 marks)

Start with xn

Find the value of xn+1

by using the formula

xn+1 = 10𝑥𝑛

3+6

15𝑥𝑛2+3

If xn+1 = xn rounded to 5 d.p.

then stop. If xn+1 ≠ xn rounded

to 5 d.p. start again using xn+1.

16

Question 16.

O is the centre of the circle.

Prove that:

(a) Angle DCO = 90 – 1

4x

(3)

(b) Angle BOC = 180 – 1

2x

(2)

(Total 5 marks)

A

B

C

D

O

1

4𝑥

17

Question 17.

Mostafa rolls a ball down a hill and records its velocity.

He plots the results on the velocity-time graph shown below.

Calculate the average speed of the ball.

Give your answer to 1 significant figure.

…………………………………………….

(Total 4 marks)

18

Question 18.

The diagram shows a pyramid with base ABC.

CD is perpendicular to both CA and CB.

Angle CBD = 39° Angle ADB = 45° Angle DBA = 55°

BC = 18 cm.

Calculate the size of the angle between the line AD and the plane ABC.

Give your answer correct to 1 decimal place.

(Total 5 marks)

19

Question 19.

The diagram shows how three identical tennis balls fit exactly inside a cylinder.

Find the percentage of the volume of the cylinder which is occupied by the tennis balls.

Give your answer to 1 decimal place.

(Total 5 marks)

TOTAL FOR PAPER IS 80 MARKS

Volume of sphere = 4

3𝜋𝑟3

2.7cm

8.1cm